{
  "abstract": "Kelly's conjecture asks whether every regular tournament admits a Hamilton cycle decomposition. Motivated by its symmetry-preserving extension, we study cyclic Hamilton decompositions of carousel tournaments. For an odd integer $n$, let \\[ T_n=\\Cay\\left( \\mathbb Z_n,\\left\\{1,2,\\ldots,\\frac{n-1}{2}\\right\\} \\right) \\] be the carousel tournament. We ask whether $T_n$ has a Hamilton decomposition invariant under translation by $1$. Although the answer is immediate when $n$ is prime, composite orders introduce a genuine obstruction: nonunit differences generate short cycles rather than Hamilton cycles. We resolve a general composite-order family by proving that, whenever $n=pq$ for primes $7\\le p<q$, the tournament $T_n$ admits a cyclic Hamilton cycle decomposition. The proof combines Hamiltonian difference sequences over prime fields with a matching argument that constructs two base paths with disjoint difference sets in $\\mathbb Z_{pq}$. Thus our result gives an infinite family supporting the cyclic, symmetry-preserving extension of the Hamilton decomposition problem for regular tournaments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07102",
  "author_total": 4,
  "authors": [
    {
      "name": "Hongci Liao"
    },
    {
      "name": "Yongju Peng"
    },
    {
      "name": "Guang Li"
    },
    {
      "name": "Yingbin Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/719kd89r99vyh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07102",
  "fulltext_url": null,
  "id": "719kd89r99vyh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07102",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7221015483",
  "pdf_url": "https://arxiv.org/pdf/2610.07102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/719kd89r99vyh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Cyclic Hamilton Cycle Decompositions of Carousel Tournaments of Order $pq$",
  "title_text": "Cyclic Hamilton Cycle Decompositions of Carousel Tournaments of Order pq",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/719kd89r99vyh",
  "venue": "arXiv",
  "versions": []
}